I posted in a couple of random threads, silly games and such, and now they're appearing in my list of 'new replies to my posts', even though I'd probably never post there again. Is there any way to set a thread so it stops feeding you updates of that sort? I didn't see anything in the Profile, and it's not a Bookmark.

I use the "Show unread posts since last visit." This allows you to select Boards (in your profile) that will specifically show up in this feature. So, select those Board where you want to see new posts and you have a custom list. You can't do it at the thread level, for now you would have to use Bookmarks or Notify for this.